BIO-SURVEILLANCE: DETECTION AND MITIGATION OF DISEASE OUTBREAKS

Transcription

1 BIO-SURVEILLANCE: DETECTION AND MITIGATION OF DISEASE OUTBREAKS A Thesis Presented to The Academic Faculty by Mi Lim Lee In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the School of Industrial and Systems Engineering Georgia Institute of Technology December 2013 Copyright c 2013 by Mi Lim Lee

2 BIO-SURVEILLANCE: DETECTION AND MITIGATION OF DISEASE OUTBREAKS Approved by: Professor David Goldsman, Advisor School of Industrial and Systems Engineering Georgia Institute of Technology Professor Seong-Hee Kim, Advisor School of Industrial and Systems Engineering Georgia Institute of Technology Professor Kwok-Leung Tsui, Advisor Department of Industrial Engineering City University of Hong Kong Professor Sigrun Andradottir School of Industrial and Systems Engineering Georgia Institute of Technology Professor Roshan Joseph Vengazhiyil School of Industrial and Systems Engineering Georgia Institute of Technology Date Approved: 6 September 2013

3 To my awesome husband and family. iii

4 ACKNOWLEDGEMENTS Pursuing my Ph.D. degree would be remembered as the most challenging but exciting journey in my life. Every moment of the journey has been shared with many great people and I would like to thank them for their support. I would like to express the deepest appreciation to my advisors, Dr. David M. Goldsman, Dr. Seong-Hee Kim, and Dr. Kwok-Leung Tsui. I have learned a lot from their vision, enthusiasm, and immense knowledge during my doctoral program. This dissertation would not have been finished without their guidance and encouragement. Besides my advisors, I would like to thank the rest of my thesis committee, Dr. Sigrún Andradóttir and Dr. Roshan Vengazhiyil, for their insightful questions and helpful suggestions. My thanks also go to my friends: Dong Gu Choi, Seonghye Jeon, Judy Sunyoung Lee, Haewon Park, Hin Kyeol Woo, THEM, and many other fellow students in the Industrial and Systems Engineering department. They were the sources of all the laughter, joy, and fun in my graduate life. My parents, Gweon Heui Lee and Kyung Ae Kim, deserve my sincere thanks for giving me a birth at the first place. Their endless love has supported me even in the sleepless nights I was struggling with my research. Last but not least, special thanks to my husband, Chuljin Park, and my first child, Dodo, who enrich my life. I look forward to starting a whole new journey with them after my Ph.D. iv

5 Contents DEDICATION iii ACKNOWLEDGEMENTS iv LIST OF TABLES vii LIST OF FIGURES ix SUMMARY xi I INTRODUCTION II REACTIVE STRATEGIES FOR DEVELOPING OUTBREAKS OF PANDEMIC INFLUENZA Simulation Model Disease Transmission Model Intervention Strategies Economic Cost Estimation Simulation Results Discussion III SPATIOTEMPORAL BIOSURVEILLANCE: CONTROL LIMIT APPROXIMATION AND THE IMPACT OF SPATIAL CORRE- LATION Background Design of the JMCUSUM Chart Fixed Scan Radius Variable Scan Radius Approximation Accuracy Experimental Setup Range of the Scan Radius Results for the Fixed Scan Radius Case Results for the Variable Scan Radius Case v

6 3.4 Impact of Spatial Correlation on Detection Performance Outbreak Radius Spatial Correlation Conclusions IV ROBUST DISTRIBUTION-FREE MCUSUM CHARTS FOR SPA- TIOTEMPORAL BIOSURVEILLANCE IN THE PRESENCE OF SPATIAL CORRELATION Background and Motivation Notation and Problem Motivation RMCUSUM Charts RMCUSUM Chart for the Fixed Scan Radius RMCUSUM Chart for the Variable Scan Radius Experiments Experimental Setup Accuracy of Control Limits ARL 1 Performance Conclusions V CONTRIBUTIONS APPENDIX A APPENDIX B APPENDIX C REFERENCES vi

7 List of Tables 1 Per-contact influenza transmission probabilities within contact groups 11 2 Age-group-specific illness attack rates and calibrated attack rates Attack rates and total costs of interventions with 35% vaccination coverage Attack rates and total costs of interventions with 70% vaccination coverage Proportions of influenza cases at high risk for complications Outpatient visit, hospitalization, and death rates Outpatient visit, hospitalization, and death costs Costs (in US$) and impacts of vaccination r versus k when δ = 1 and ρ = Empirical h (Analytical h ) when r is fixed Empirical ARL 0 of the JMCUSUM-F chart with analytical h Empirical ARL JF 1 (Analytical ARL JF 1 ) with analytical h Empirical ARL 0 for the SMCUSUM chart with analytical h r Empirical ARL JV 1 (ARL S 1) Identification accuracy CP (SP) with Σ Identification accuracy CP (SP) with Σ Configurations Empirical ARL 0 from the multivariate normal data Empirical ARL 0 from the multivariate Poisson data ARL 1 from multivariate normal data ARL 1 from multivariate Poisson data ARL 1 comparison Average age-stratified overall illness attack rates (%) and cost estimates Empirical ARL 0 of the JMCUSUM-F chart with analytical h Empirical (analytical) ARL JF 1 with analytical h vii

8 26 Empirical ARL 0 for the SMCUSUM chart with analytical h r Empirical ARL JV 1 (ARL S 1) viii

9 List of Figures 1 Age distribution for simulated population Household size distribution for simulated population Simulation flowchart and modeled influenza natural history Total cost of intervention strategies vs. the average illness attack rate 23 5 Daily attack rates Illness attack rates for modeled interventions with 35% vaccine coverage 26 7 Illness attack rates for modeled interventions with 70% vaccine coverage 27 8 Total cost of modeled intervention strategies vs. average illness attack rate Coordinate expression of regions (p = 7 7) Outbreak clusters when c out = 25 (outbreak regions are in gray) Correlation settings of Σ 1 and Σ 2 for region Empirical ARL 0 Target ARL 0 (%) versus r for a single MCUSUM chart Empirical ARL 0 Target ARL 0 (%) versus k for a single MCUSUMchart Empirical ARL 0 Target ARL 0 (%) versus r for the JMCUSUM-F chart Spatial correlation vs. ARL 1 and CP with δ = 1 and Σ Coordinate expression of regions (p = 7 7) The RMCUSUM f chart The RMCUSUM v chart D ρ vs A ρ Estimation of A ρ Finding ǔ Outbreak clusters when c out = 25 (outbreak regions are in gray) Correlation settings of Σ 1 and Σ 2 for region Σ 3 and Σ Empirical ARL 0 Target ARL 0 (%) versus r for a single MCUSUM Empirical ARL 0 Target ARL 0 (%) versus k for a single MCUSUM ix

10 27 Empirical ARL 0 Target ARL 0 (%) versus r for the JMCUSUM-F chart x

11 SUMMARY In spite of the remarkable development of modern medical treatment and technology, the threat of pandemic diseases such as anthrax, cholera, and SARS has not disappeared. As a part of emerging healthcare decision problems, many researchers have studied how to detect and contain disease outbreaks, and our research is aligned with this trend. This thesis mainly consists of two parts: epidemic simulation modeling for effective intervention strategies and spatiotemporal monitoring for outbreak detection. We developed a stochastic epidemic simulation model of a pandemic influenza virus (H1N1) to test possible interventions within a structured population. The possible interventions such as vaccination, antiviral treatment, household prophylaxis, school closure and social distancing are investigated in a large number of scenarios, including delays in vaccine delivery and low and moderate efficacy of the vaccine. Since timely and accurate detection of a disease outbreak is crucial in terms of preparation for emergencies in healthcare and biosurveillance, we suggest two spatiotemporal monitoring charts, namely, the SMCUSUM and RMCUSUM charts, to detect increases in the rate or count of disease incidents. Our research includes convenient methods to approximate the control limits of the charts. An analytical control limit approximation method for the SMCUSUM chart performs well under certain conditions on the data distribution and monitoring range. Another control limit approximation method for the RMCUSUM chart provides robust performance to various monitoring range, spatial correlation structures, and data distributions without intensive modeling of the underlying process. xi

12 Chapter I INTRODUCTION With the ongoing threat of pandemic diseases and bioterrorism, extensive research efforts have been undertaken on the design and performance of disease outbreak surveillance systems and mitigation strategies. Various models, originating from different research fields, have been proposed for analyzing and estimating the spread of past and future pandemics. Epidemic simulation models that mimic events happening in the real world without making strong assumptions provide useful tools to increase our understanding of the dynamics and patterns of disease propagation. They also allow for the study and evaluation of the potential impacts of various government policies and intervention strategies for infectious diseases, including vaccination, prophylactic use of antivirals, and social distancing strategies such as school closure, quarantine, and isolation. Over the last several years, these simulation models have been influential in the formation of pandemic preparedness plans. A simulation can explore not only the epidemiological impact but also the economic effectiveness of additional, reactive strategies for containing disease outbreaks. Some of the challenges pertaining to such simulation models can be summarized as follows. A simulation model must imitate the complicated real world. The population and community structure designed for the simulation should be able to capture the characteristics of a targeted population and the population s behaviors. For example, places of exposure, such as households, schools, and workplaces, should be carefully selected by observing the population and the community structures closely. To this end, a great deal of demographic input data are often required. 1

13 The model logic and interventions depend on the builder s purpose, social situations encountered, and disease characteristics. The builder needs to determine what kinds of interventions can be employed and how to apply them in the model. For example, the availability and amount of vaccines/antivirals can be affected by the wealth of the country and the disease dynamics. The distribution of the vaccines/antivirals can be affected by political or geographical supply chain issues. One must also study the exposure frequencies and times of individuals, such as contact rates and contact durations, as well as the disease transmission parameters such as the probability that an infected person will infect a healthy person given their contacts. For these tasks, knowledge ranging from sociology to epidemiology may be required. The model is carefully calibrated to predict illness attack rates to calculate costs resulting from applied interventions. This is where the validity of the simulation matters. It is difficult to track a relationship between illness attack rates and costs. In addition, both direct and indirect costs should be considered. One may find it difficult to obtain appropriate references for these costs. A goal in this thesis is to develop a reasonable epidemic simulation model that can test possible interventions for a structured community. The model should be able to report valid estimates of illness attack rates and costs associated with the different combinations of mitigation strategies. This type of model will be quite helpful for public health authorities when reacting to future outbreaks of pandemics. The timely and accurate detection of a disease outbreak is crucial for preparation for emergency situations. Before any studied mitigation strategies are performed, one must alarm (signal) an outbreak at an appropriate time, and decide when and where to apply the mitigation strategies. 2

14 One of the statistical approaches developed for timely outbreak detection is statistical process control (SPC) charts. Cumulative sum (CUSUM) charts have been especially popular in public health surveillance to detect increases in the rate or counts of disease incidents. However, the use of CUSUM charts in biosurveillance can be challenging when compared to the conventional SPC charts in other application areas. Possible challenges and opportunities include the following issues. Since the disease outbreak is a spatiotemporal event, the surveillance method should detect the time when an outbreak occurs as well as the coverage of the outbreak. Fast and accurate detection is important and preferred. Also, the performance of the method should be evaluated with respect to detection time and accuracy. Correlation may exist in observed data. This could be in the form of spatial correlation, autocorrelation (over time), or both. A detection method that can take advantage of the correlation, or at least can be applied to the correlated data, is needed. The complexity in designing CUSUM charts often relates to the dimensionality of monitoring regions. The control limits of the CUSUM charts are typically calibrated by trial-and-error simulation, but this task can be extremely timeconsuming and challenging if the number of monitoring regions is large. Surveillance through the CUSUM charts requires intensive modeling of the monitoring system that changes according to the input parameters and the underlying data distribution (which is often unknown). In this thesis, we focus on spatiotemporal multivariate CUSUM (MCUSUM) charts to detect a disease outbreak. In order to avoid tedious simulations to calibrate the MCUSUM charts, we first propose MCUSUM charts whose control limits 3

15 are approximated analytically by assuming the charts are independent; and then we will expand our research to make the charts applicable to any data distribution, even in the presence of the correlation among the charts. Chapter 2 introduces a stochastic model to investigate realistic strategies that can be used in reaction to emerging outbreaks of pandemic influenza. The model is constructed to represent a typical mid-sized North American city, and calibrated to documented illness attack rates. Reduced attack rates and economic costs due to the intervention strategies are estimated. Chapter 3 reviews MCUSUM charts based on sequential likelihood ratio tests in the presence of spatial correlations, and then proposes an analytical method that approximates the control limits, making the design of the MCUSUM charts much more convenient. We also study how spatial correlation impacts the scheme s outbreak detection performance. Chapter 4 studies another class of MCUSUM chart that can be robust to any underlying distribution of data in the presence of spatial correlation. The chart provides reliable performance by overcoming certain restrictions of the MCUSUM charts developed in Chapter 3. Chapter 5 summarizes the main contributions of the thesis. 4

16 Chapter II REACTIVE STRATEGIES FOR DEVELOPING OUTBREAKS OF PANDEMIC INFLUENZA In April, 2009, the World Health Organization (WHO) announced the emergence of a new influenza A (H1N1) virus, and on June 11, 2009, it declared that the world was at the start of a new influenza pandemic [68]. WHO reported more than 414,000 laboratory-confirmed cases of H1N1 [67] a gross underestimate, as many countries simply stopped counting individual cases. The U.S. Centers for Disease Control and Prevention reported widespread influenza activity in forty-six states, with influenzalike illness (ILI) activity in October 2009 higher than what is seen during the peak of many regular flu seasons; and further, Almost all of the influenza viruses identified... are 2009 H1N1 influenza A viruses [7]. Countries found themselves in the position of having to react to contain already developing Fall outbreaks of influenza due to the new pandemic strain, a position they are likely to find themselves in again if and when future waves of pandemic influenza occur. Research has suggested that mass vaccination of 60 70% of the population prior to the start of the flu season could effectively contain outbreaks due to pandemic strains [12, 17, 29, 69]; and the public health preparedness plans of most countries have, accordingly, emphasized vaccination intervention strategies. However, the recent experience with H1N1 suggests that high vaccination coverage levels are difficult to achieve. In the case of H1N1, vaccination programs in most northern hemisphere countries started only after the virus was widely circulating. Furthermore, in some countries, supplies of vaccine were limited [9], delivery and administration occurred over a period of several months [37, 42], and there were reports of public skepticism 5

17 regarding the necessity and safety of vaccination [36, 38], all of which were strong indicators suggesting that high vaccination coverage would be difficult to achieve. While many institutions in the U.S. and elsewhere strongly encouraged and, in some cases, required workers to be vaccinated against seasonal influenza in 2009, H1N1 vaccination guidelines were focused mostly on people in certain age and high-risk groups [8]. Delays, limited and untimely vaccination supplies, and public reluctance to be vaccinated are likely to reduce the effectiveness of vaccination campaigns [17, 69]. The issues outlined above for the recent outbreak of H1N1 are likely to occur again in future outbreaks of pandemic influenza. In this chapter, we explore the effectiveness of realistic reactive intervention strategies implemented after the beginning of outbreaks of pandemic influenza. We calibrate our model based on data for the H1N1 pandemic (see Tuite et al. [63]), and we investigate the impacts of (i) the moderate vaccination coverage levels which, based on past experience, are likely to be realized, as well as high levels which would be more ideal; (ii) very limited treatment of cases with antivirals and prophylaxis of cases households with antivirals; and (iii) limited and practical social distancing measures such as five-day closure of individual schools on an as-needed basis, encouragement of liberal leave policies in the workplace, and encouragement of self-isolation. Intervention strategies that combine these approaches are also studied (cf. Halloran et al. [18]). For all intervention strategies, we provide cost estimates associated with morbidity and mortality that take into account direct medical costs as well as economic consequences resulting from school closures and work loss. The research conducted in this chapter has been published in Andradóttir et al. [2] Simulation Model We developed a portable and adaptable stochastic, individual-level simulation model of influenza spread within a structured population. The simulator is similar to models 6

18 developed by Longini et al. [29, 30]. A simulated population of 649,565 people was generated stochastically to represent a typical North American city, namely, Hamilton (Ontario), Canada, which was chosen due to availability of demographic and epidemiological data necessary for constructing and calibrating the simulator. Our population is a collection of heterogeneous individuals with various attributes that impact whom they interact with (and hence whom they may infect or get infected by). More specifically, each individual has the following stochastically generated attributes: age, household, playgroup or daycare attended (for pre-school children), school attended (for school-age children), workgroup (for working adults), household census tract and workplace census subdivision, community, and neighborhood. As in Longini et al. [30], a community consists of approximately 2000 people living within the same census tract, and a neighborhood consists of approximately 500 people living within proximity to each other within the same community; also see the recent papers including Aleman et al. [1] and Stroud et al. [57], which incorporate more-detailed individual-level behavior involving larger populations. Age and household-size distributions, shown in Figures 1 and 2, were matched to 2001 Canadian census data [54, 55]. Household census tract assignments were made so that census tract population sizes were consistent with 2006 census statistics [51]. Each individual belongs to three or four contact groups. In particular, each individual belongs to a household, neighborhood, and community. In addition, children younger than 16 belong to either a playgroup, daycare, or school, depending on age; most children in age range belong to a school or workgroup; and most adults in age range belong to a workgroup. Preschool children were categorized as belonging to a playgroup/daycare, each with 50% probability. We separated secondary schools into middle schools and high schools based on grade to allow different contact group sizes and to make our model more representative of mid-sized U.S. cities. The numbers of playgroups, daycares, elementary, middle, and high schools in each 7

19 Figure 1: Age distribution for simulated population Figure 2: Household size distribution for simulated population 8

20 community were based on Longini et al. [30], and were combined with the number of individuals in each category in our simulation population to obtain the contact group sizes. Workgroups were formed to match 2006 employment statistics [53] as well as census statistics on the geographical distribution of workers [52]. The number of working adults (19 59 years old) was based on census data [52]; and the number of working children (16 18 years old) was based on Ontario data on drop-out rates [5] and the employment rate for ages [52]. Rather than representing entire workplace institutions, we formed workgroups of size 20 to represent the typical number of coworkers an individual is likely to have close contact with during the day. Average playgroup, daycare, and lower and upper secondary school (i.e., middle and high school) contact group sizes were chosen following similar reasoning Disease Transmission Model The simulator models influenza transmission over a 180-day period, within the contact groups previously defined. To initiate influenza outbreaks, simulations are seeded with approximately 100 randomly selected initial infectives, with all other individuals considered susceptible (state 0). Susceptible people are assumed to have daily contacts with other individuals in their contact groups, i.e., their household and school or workgroups, as well as with people in their neighborhood and community. Susceptible people have the opportunity, each day, to become infected in their contact groups. The daily probability of infection for each susceptible person is determined by the number of infectious contacts in his contact groups, and on the per-contact probability of transmission for each type of contact. For example, the probability of a susceptible child who attends daycare being infected on a particular day is: 1 [ Pr(child is not infected in the household) Pr(child is not infected in the neighborhood) 9

21 Pr(child is not infected in the community) Pr(child is not infected at the daycare center) ]. Within each contact group, the probability of infection of a susceptible individual depends on the number of infectious individuals in the group. For example, suppose that k 1 children and k 2 adults in a household are infectious on a particular day. Then the probability of a susceptible household member being infected in that household on that day is: 1 [ Pr(not infected by a child in the household) k 1 Pr(not infected by an adult in the household) k 2 ]. The number of infectious people in the contact groups (e.g., k 1 and k 2 ), are random variables that are updated at the beginning of each day. Infection of susceptibles depends on the number of infected persons in their contact groups, on the vaccine and antiviral-use status of susceptibles and their infectious contacts, and on age- and contact-group-specific per-contact transmission probabilities (Table 1). The probability that infection is transmitted from an infected person to a susceptible person also depends on whether the infectious person is symptomatic or asymptomatic. Table 1 shows the rates for symptomatic individuals. The transmission rates for asymptomatic individuals are half of those shown in Table 1. These probabilities are based on Longini et al. [29, 30], with adjustments made to calibrate baseline (no intervention) results. 10

22 Table 1: Per-contact influenza transmission probabilities within contact groups Contact Group Transmission Probability Household 1 Child-to-child 0.8 Child-to-adult 0.3 Adult-to-child 0.3 Adult-to-adult 0.4 Community 2 Pre-schooler School child Adult (ages 19 52) Adult (ages 53+) Daycares/Playgroups 2 Daycares Playgroups Schools 2 Elementary schools Middle schools High schools Workgroups Within households, the probability that a symptomatic child (age 18 years or less) infects a susceptible child is 0.8; that a symptomatic child infects a susceptible adult (at least 19 years old), or that a symptomatic adult infects a susceptible child, is 0.3; that a symptomatic adult infects a susceptible adult is 0.4 [30]. 2 Probability that a susceptible person in the age or school group is infected through contact with a symptomatic person in the group. 11

23 Table 2: Age-group-specific illness attack rates and calibrated attack rates Simulated illness attack rates by the percentage of adults 53+ years old with pre-existing immunity 1 Calibrated attack rates (AR) Age 30% 50% 70% Age AR % 31.0% 30.8% % % 55.0% 55.2% % % 57.1% 57.3% % 49.7% 49.7% % % 39.8% 39.3% % 15.3% 8.8% % % 13.2% 7.5% % Overall 36.8% 35.4% 33.5% Overall 34.1% 1 See the discussion in Tuite et al. [62]. The simulator is calibrated to match documented illness attack rates and basic reproduction numbers (R 0 ), defined as the number of cases one case generates on average over the course of its infectious period. Baseline (no-intervention) scenario age-group-specific attack rates were derived using 2009 estimates for the H1N1 basic reproduction number in Ontario [20, 62, 63] (see Table 2). These rates take into account reduced risk in adults born prior to 1957 [20]. A compartmental model parameterized in this way was well-calibrated to observed attack rates during the Fall pandemic wave in Ontario [62]. The simulator s R 0 value of 1.4 is also consistent with other published reports such as Fraser et al. [13], New Scientist [35] and Yang et al. [69]. Figure 3 depicts a flowchart of the model. The modeled natural history and simulator dynamics parameters, described below and shown in Figure 3, were based on Longini et al. [29, 55]. People infected with influenza first pass through a 1 3 day latent / incubation period (state 1; average length 1.9 days), during which they do not have influenza symptoms. They are not infectious until the last day of the period; at that point, they become half as infectious as if they were to develop 12

24 Figure 3: Simulation flowchart and modeled influenza natural history symptoms in the subsequent period. During that subsequent infectious period, 67% will develop influenza symptoms (state 2), and 33% will be asymptomatic (state 3). Symptomatic infectives are assumed to be twice as infectious as asymptomatics, and have a chance of withdrawing home during each day of illness; upon withdrawal, they only make contacts within their household and neighborhood, with transmission probabilities doubled in the household contact group, until they recover. If a school child withdraws home due to illness, one adult in the household also stays home. Each day in states 2 and 3, an infectious person has a chance to exit the state and be removed from the simulation (i.e., to recover or die state 4). Probabilities for transition into and out of states are given in Figure 3 and are based on Longini et al. [29, 30]. 13

25 2.1.2 Intervention Strategies We modeled a baseline case where no intervention takes place, along with strategies representing various combinations of vaccination, antiviral treatment and household prophylaxis, school closure, and general social distancing (see the results in Tables 3 and 4 and Table 23 provided in the Appendix A). Each component of the strategies is described in detail below. Interventions are triggered in a particular simulation run when the overall illness attack rate reaches 0.01%. Twenty runs of the simulator were performed for each intervention strategy, from which average illness attack rates were calculated. We briefly describe the interventions under consideration. Vaccination: We model both pre-vaccination as well as reactive strategies, with reactive vaccination programs beginning immediately, 30 days, or 60 days after the trigger. The delays model disruptions in vaccine production and supply chains. We allow enough doses to cover either 35% or 70% of the population. In reactive strategies, we consider cases where (i) all vaccines become available at the same time, and (ii) the doses become available in three equal-sized batches, two weeks apart, due to additional production and supply-chain disruptions. Vaccine efficacy refers to the reduction, after vaccination, in the probability of becoming infected due to contact with an infected person (VEs), or to the reduction, after vaccination, in the probability of infecting a susceptible contact (VEi). Vaccine efficacy does not refer to the fraction of individuals having an immunogenic response to the vaccine (which is typically much larger than our measures). We study a low-efficacy single-dose vaccine (efficacy against susceptibility to infection, VEs = 0.3, and efficacy against infectiousness, VEi = 0.2) as well as a moderate-efficacy vaccine (VEs = 0.4, VEi = 0.5) [3]. Each day, our model randomly vaccinates any remaining unvaccinated individuals who are either uninfected or in the latent or asymptomatic phases of infection, all with equal probability based on the number of available doses. Moreover, protection from the vaccine builds over time, with 50% of the vaccine s efficacy realized upon vaccination, 14

26 and full protection after two weeks. Antiviral Treatment and Household Prophylaxis: We investigate strategies involving treatment of infected individuals with a five-day course of antivirals, as well as strategies that also allow for ten-day prophylaxis of the infected individuals household members. We assume that 1% of individuals do not complete their course. We use an antiviral efficacy against susceptibility (AVEs) of 0.3 and against infectiousness (AVEi) of 0.7 [30]. Individuals receive direct benefit from antivirals only while they are taking them. Antiviral use is considered alone and in combination with other intervention strategies. It is assumed that antiviral courses are available for 10% of the population and that they are distributed to infected individuals and their household members until the supply is exhausted. School Closure and Social Distancing: We implement a rolling school closure model, where a daycare or school closes for five days if five or more cases are identified in that group. Given that infected individuals are on average infectious for 4.1 days (see Figure 3), closing schools for fewer than 5 days is unlikely to be very effective. It is possible for these groups to close more than once during the simulation. We also model a reduction in workplace and general community contacts of 20% (i.e., 20% of infected individuals in each contact group will not infect other members of the group). This represents the exercise of a general level of caution, including a modest limitation of contacts within workgroups (e.g., by invoking occasional telecommuting and other self-limiting behaviors, holding fewer large meetings, etc.) and also within the general community (e.g., reduction in attendance in social groups and larger community events, etc.). 15

27 Table 3: Attack rates and total costs of interventions with 35% vaccination coverage Intervention 1 Delay in initiation of vaccination 2 No post-initiation vaccination delays Post-initiation vaccination delay 3 Attack rate (%) Cost (US$m) Attack rate (%) Cost (US$m) None A S A+S V L Pre-vaccination V L Reactive, no delay V L 30-day delay V L 60-day delay V M Pre-vaccination V M Reactive, no delay V M 30-day delay V M 60-day delay V L +A Pre-vaccination V L +A Reactive, no delay V L +A 30-day delay V L +A 60-day delay V M +A Pre-vaccination V M +A Reactive, no delay V M +A 30-day delay V M +A 60-day delay V L +S Pre-vaccination V L +S Reactive, no delay V L +S 30-day delay V L +S 60-day delay V M +S Pre-vaccination V M +S Reactive, no delay V M +S 30-day delay V M +S 60-day delay V L +A+S Pre-vaccination V L +A+S Reactive, no delay V L +A+S 30-day delay V L +A+S 60-day delay V M +A+S Pre-vaccination V M +A+S Reactive, no delay V M +A+S 30-day delay V M +A+S 60-day delay Abbreviations for modeled interventions: V (vaccination of up to 35% of the population), L (low efficacy), M (moderate efficacy), A (antiviral treatment and household prophylaxis of up to 10% of the population), S (school closure and social distancing). 2 Initial supply-chain delays which prevent immediate initiation of vaccination programs after the intervention trigger occurs. 3 Additional supply-chain delays, after initiation of the vaccination program, as a result of which vaccines become available in three equal batches, spaced two weeks apart. 16

28 Table 4: Attack rates and total costs of interventions with 70% vaccination coverage Intervention 1 Delay in initiation of vaccination 2 No post-initiation vaccination delays Post-initiation vaccination delay 3 Attack rate (%) Cost (US$m) Attack rate (%) Cost (US$m) V L Pre-vaccination V L Reactive, no delay V L 30-day delay V L 60-day delay V M Pre-vaccination V M Reactive, no delay V M 30-day delay V M 60-day delay V L +A Pre-vaccination V L +A Reactive, no delay V L +A 30-day delay V L +A 60-day delay V M +A Pre-vaccination V M +A Reactive, no delay V M +A 30-day delay V M +A 60-day delay V L +S Pre-vaccination V L +S Reactive, no delay V L +S 30-day delay V L +S 60-day delay V M +S Pre-vaccination V M +S Reactive, no delay V M +S 30-day delay V M +S 60-day delay V L +A+S Pre-vaccination V L +A+S Reactive, no delay V L +A+S 30-day delay V L +A+S 60-day delay V M +A+S Pre-vaccination V M +A+S Reactive, no delay V M +A+S 30-day delay V M +A+S 60-day delay Abbreviations for modeled interventions: V (vaccination of up to 70% of the population), L (low efficacy), M (moderate efficacy), A (antiviral treatment and household prophylaxis of up to 10% of the population), S (school closure and social distancing). 2 Initial supply-chain delays which prevent immediate initiation of vaccination programs after the intervention trigger occurs. 3 Additional supply-chain delays, after initiation of the vaccination program, as a result of which vaccines become available in three equal batches, spaced two weeks apart. 17

29 2.2. Economic Cost Estimation We determine economic costs associated with the influenza outbreaks and modeled intervention strategies. We include medical spending due to illness, costs of antivirals and vaccines, and costs associated with teachers and other working adults staying home due to their own illness, illness of dependent children, or due to school closure. Medical spending includes co-payments and net payments for outpatient visits and hospitalization, as well as prescription and over-the-counter medications for influenza and complications or secondary infections. Costs are stratified by age-group and by low- or high-risk status of individuals with respect to complications of influenza. We also include the present value of earnings lost due to premature mortality. Cost estimates and probabilities of risk status and of complications and death were taken from Meltzer et al. [33], with costs inflated using 2008 consumer price index and medical price index estimates [6, 23, 32, 58]. These costs are combined with the data on age-specific attack rates, utilized vaccination doses, and days of school closure obtained from our simulation model. The total cost of each intervention scenario includes the cost of vaccine doses and antiviral courses used, if any; costs associated with parents staying at home with sick children and school teachers, parents, and children staying home due to school closure; costs due to illness-related absence from work; medical costs associated with illness, including outpatient visits, prescription and over-the-counter drugs, and hospitalization; and lost earnings due to death. We use methods described by Meltzer et al. [33] to quantify most medical and work-loss costs (see also Medlock and Galvani [32]). Table 5 shows the proportions of illnesses assumed to be at high risk for complications among children (0 18 years old), younger adults (19 59 years old) and seniors (over 60). Table 6 shows estimated rates of outpatient visits, hospitalizations, and death used in our calculations for children, adults, and seniors at high risk and not at high risk of complications. We chose the 18

30 Table 5: Proportions of influenza cases at high risk for complications 1 Age Group Proportion at high risk Children (0 18) Adults (19 59) Seniors (60+) Proportions taken from Meltzer et al. [33], and adapted to our age groups. Table 6: Outpatient visit, hospitalization, and death rates 1 Rates per 1000 persons ill Outpatient visits Hospitalization Deaths Not at high risk Children Adults Seniors High risk Children Adults Seniors Rates taken from Meltzer et al. [33] low rate estimates presented in Meltzer et al. [33], which we believe to be most consistent with the relatively low R 0 (1.4) for our model. Frequency and costs (in US$) associated with influenza-related outpatient visits, hospitalizations, and deaths are shown in Table 7. All the above costs were combined with age-specific attack rates obtained from our simulation model. In addition, we assume average costs of $25 per vaccine dose or antiviral course used, consistent with previous reports [48]. Table 8 shows other costs associated with vaccination (i.e., the cost of lost time, travel, and side effects). These costs are based on Bowlby [5], inflated as described above. The vaccination costs are combined with the number of used vaccination doses obtained from our simulation model. We assume that 1% of antiviral users discontinue use due to side effects; medical and other costs associated 19

31 with these side effects are not included in our model. To estimate costs of ill individuals staying home and work-loss associated with parents staying at home with sick children, we multiplied the number of days (obtained from our simulation model) with the inflation-adjusted average value of lost days from Table 7. Similarly, we estimated the average number of teachers at schools and daycares by dividing the total number of such teachers in Hamilton [56] among the schools and daycares in our model. To estimate the cost of lost teacher productivity due to school closures, we multiplied the number of days schools and daycares are closed in our simulation model by the average number of teachers at Hamilton schools and daycares and by the average value of a day of lost work obtained from Table 7. Table 23 in the Appendix A shows age-stratified and overall illness attack rates for all modeled scenarios, along with total cost estimates. Figure 4 depicts the total cost (US$m) plotted vs. average overall illness attack rate (%) for each intervention. 20

32 Table 7: Outpatient visit, hospitalization, and death costs 1 Age group Outcome category item Children Adults Seniors Outpatient Visits Average no. visits per case Net payment per visit $80.90 $62.74 $82.55 Average copayment for outpatient visit $8.26 $6.60 $6.60 Net payment per prescription $41.28 $59.44 $59.44 Average prescriptions per visit Average copayment per prescription $4.95 $4.95 $4.95 Days lost Value of 1 day lost $91.85 $ $91.85 Subtotal: Per-case Outpatient Costs $ $ $ Hospitalization Hospital cost $4, $9, $11, Net payment per outpatient visit $ $ $ Average copayment for outpatient visit $8.26 $6.60 $6.60 Net payment for drug claims $42.93 $69.34 $67.69 Most likely days lost Value of 1 day lost $91.85 $ $91.85 Subtotal: Per-case Hospitalization Costs $5, $11, $12, Deaths Average age (years) PV earnings lost $1,435,750 $1,466,231 $93,027 Most likely hospital costs $5,671 $12,555 $13,718 Subtotal $1,441,422 $1,478,788 $106,746 Ill but no medical care sought Days lost Value of 1 day lost $91.85 $ $91.85 Over-the-counter drugs $3.30 $3.30 $3.30 Subtotal: Per-case ill (no care sought) $ $ $ Estimates based on figures from Meltzer et al. [33]. Cost estimates inflated by 2008 consumer and medical price indices [6, 23, 58] as appropriate. 21

33 Table 8: Costs (in US$) and impacts of vaccination 1 Item Probability of side effect Per-case cost of side effect Cost scenario (per patient) Assumed cost of vaccination $25.00 Patient time $5.65 Patient travel costs $5.65 Side effect Mild $94 $5.04 Guillain-Barre Syndrome (GBS) $100,800 $0.33 Anaphylaxis $2,490 $ Estimates based on figures from Meltzer et al. [33]. Travel and side effect cost estimates inflated by 2008 consumer and medical price indices [6, 23, 58] as appropriate Simulation Results With no intervention, the average overall illness attack rate is 34.1%, with an estimated total cost of $81.1 million (Table 3). Pre-vaccination of 35% of the population with a low-efficacy vaccine reduces the average overall illness attack rate to 26.1% (total cost $71.1 million), and with a moderate-efficacy vaccine to 18.8% (total cost $53.7 million). Not surprisingly, pre-vaccination of 70% of the population is more effective (overall average illness attack rate 12.0%, total cost $47.0 million for a lowefficacy vaccine; and 0.2% and $19.3 million with a moderate-efficacy vaccine; see Table 4). Reactive vaccination alone, of 35% of the population with a low-efficacy vaccine delivered in three batches, reduces the overall average illness attack rate to 28.8% (or 22.8% with a moderate-efficacy vaccine), with a total cost of $77.7 million ($63.1 million with a moderate-efficacy vaccine). Thirty- and 60-day delays in initiation of reactive vaccination, with vaccines delivered in three batches, result in attack rates of 29.5% (total cost $79.3 million) and 32.2% (total cost $86.0 million), respectively, for a low-efficacy vaccine, and 24.6% (total cost $67.5 million) and 30.8% (total cost $82.5 million), respectively, for a moderate-efficacy vaccine. Figure 5 shows daily 22

34 Figure 4: Total cost of intervention strategies vs. the average illness attack rate attack rates for (i) the case of 70% coverage of low-efficacy vaccine with 60-day initial delay, and (ii) the baseline case. For case (i), the vaccine is given on the 60th day followed by receipt of vaccine after two additional two-week delays (see arrows in Figure 5). Note that vaccine given on the 60th day decreases the attack rate compared to the baseline; but the two subsequent receipts of vaccine do not result in additional benefits. Clearly, with a 60-day delay, interventions occur too late in the epidemic to have any meaningful effect (see Figure 5). Antiviral use at low (10%) coverage alone results in an overall attack rate of 31.3% (total cost $75.9 million). School closure and social distancing alone result in an attack rate of 24.0%, with a total cost of $125.0 million. Suppose we combine reactive low-efficacy vaccination of 35% of the population delivered in three batches, antivirals (10% coverage), and school closure and social distancing. Then the overall average illness attack rate is 4.5% (total cost $

35 Figure 5: Daily attack rates million) if no delays occur in the initiation of vaccination, and 5.4% (total cost $36.8 million) if a 60-day delay occurs. With a moderate-efficacy vaccine, the attack rate for this last scenario reduces to 2.4% (total cost $22.0 million). Similar relationships between interventions are apparent for interventions with 70% vaccination coverage, shown in Table 4. Vaccination coverage of 70% with a moderate-efficacy vaccine, combined with antiviral treatment and school closure, is highly effective, even with an initial 60-day delay and additional supply-chain disruptions (average illness attack rate 1.4%, total cost $27.4 million). We note that the results when all vaccines are available at the same time are better than those involving delivery in batches, and sometimes significantly so, especially for a moderate-efficacy vaccine (Tables 3 and 4). Figures 6 and 7 illustrate the comparative illness attack rates of the various intervention strategies discussed above for all combinations of low/moderate-efficacy vaccine delivered in three batches and at 35%/70% coverage as a function of the initial delay in vaccination implementation due to supply-chain disruptions. The impact of vaccinating 70% of the population, 24

36 rather than 35%, ranges from moderate to substantial, with the increased coverage being most beneficial when the vaccine is delivered in a timely manner, and the vaccine is either of moderate efficacy or of low efficacy applied in combination with other intervention strategies. Complete (age-stratified and overall) average illness attack results for all modeled interventions are given in Table 23 in Appendix A. The comparative effectiveness of interventions is similar when age-group-specific results are studied. Figure 8A illustrates attack rate and total cost combinations for interventions that result in at least a 75% reduction in cost compared to no intervention. Abbreviations for modeled interventions are PV (pre-vaccination), V (vaccination), L (low-efficacy), M (moderate efficacy), 35 (35% coverage of population), 70 (70% coverage), A (antiviral treatment and household prophylaxis of up to 10% of the population), and S (school closure and social distancing). Multiple occurrences of each plotting symbol may occur; occurrences at higher costs and illness attack rates represent interventions with longer supply-chain delays. In Figure 8A, the closer to the origin, the more desirable an intervention is in terms of total cost and average illness attack rate. Aside from pre-vaccination strategies, we see that 70% reactive vaccination with a moderate-efficacy vaccine and school closure and social distancing, or even 35% reactive vaccination with a moderate-efficacy vaccine, antiviral use, and school closure, also result in substantial reductions in cost and attack rates. Figure 8B illustrates attack rate and cost results for interventions that result in more-modest 50 75% reductions in cost compared to no intervention. Once again, several strategies combining vaccination, antiviral use, and school closure/social distancing are competitive with pre-vaccination. 25